Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones
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Finding the Value of the Derivative Using a Graph
291–296 Use the graph to determine the solution.
291.
Estimate the value of f′(3) using the graph.
292.
Estimate the value of f′(–1) using the graph.
293.
Estimate the value of f′(–3) using the graph.
294.
Based on the graph of
295.
Based on the graph, arrange the following from smallest to largest: f′(–3), f′(–2), and f′(1).
296.
Based on the graph, arrange the following from smallest to largest: f′(1), f′(2), f′(5), and 0.1.
Using the Power Rule to Find Derivatives
297–309 Use the power rule to find the derivative of the given function.
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Finding All Points on a Graph Where Tangent Lines Have a Given Value
310–311 Find all points on the given function where the slope of the tangent line equals the indicated value.
310. Find all x values where the function
311. Find all x values where the function
Chapter 5
The Product, Quotient, and Chain Rules
This chapter focuses on some of the major techniques needed to find the derivative: the product rule, the quotient rule, and the chain rule. By using these rules along with the power rule and some basic formulas (see Chapter 4), you can find the derivatives of most of the single-variable functions you encounter in calculus. However, after using the derivative rules, you often need many algebra steps to simplify the function so that it’s in a nice final form, especially on problems involving the product rule or quotient rule.
The Problems You’ll Work On
Here you practice using most of the techniques needed to find derivatives (besides the power rule):
The product rule
The quotient rule
The chain rule
Derivatives involving trigonometric functions
What to Watch Out For
Many of these problems require one calculus step and then many steps of algebraic simplification to get to the final answer. Remember the following tips as you work through the problems:
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